Cutters of the above mentioned type are normally hand-operated. Sawing in asphalt and concrete floors with such hand-operated cutters, which also are referred to as power cutters or cutting machines, however is a difficult task not the least from an ergonomical point of view. Therefore, trolleys have been designed and are conventionally used for carrying the cutter during the performance of that type of work. The combination of a cutting machine which basically is intended for manual operation of the cutter, and a trolley for such machine, however, gives rise to new problems. One such problem is due to the fact that the front and rear handles of cutting machines designed for manual operation conventionally are connected to the machine body via anti-vibration means. Therefore, alignment problems can arise when using the trolley and the cutter in combination, such that the direction of the groove established by the cutting blade will deviate from the direction of movement of the trolley. Further, there is a long felt want to provide a cutting trolley which allows the provision of a more easily controlled sawing depth than has been possible with cutting trolleys used today.